I can try to help;
I spent a weekend in Tenerife, and it was honestly too short. We were in both the North and South, and it only takes 1-2 hours depending on transportation mode to get between the two parts. It also depends what you're looking for, the North is more authentic and the natural pools are beautiful. We also hiked Teide, which is the volcano on the island, and that took 3.5 hours with a half hour for lunch, and you can stay at the refugio at the summit. It is physically demanding though, so I would recommend being in good physical shape. The South is your more lay on the beach immersion, and is more touristy as well. I stayed in hostels, so would not be able to assist on hotel recommendations. You can do a cruise for a few hours, snorkel, and just wander the cities. Santa Cruz de Tenerife, the main city in the North is a little more spread out that those in the South, but I preferred it to the South.
For jumping between the islands, I believe there's a boat you can take from Gran Canaria to Tenerife, as well as fly from Ryanair. You don't need a car, although I think renting scooters or bikes would be fun. The bus system gets you anywhere in Tenerife, so I'd assume it's similar on the other islands. On Gran Canaria, there's the Maspalomas dunes, but never having been to the island, I can't expound on other suggestions.
You'll have a great time, the Canarias are beautiful. I was there in early March and we had mid-70's weather.
Alec
